What is the solution for y^{''}-4y^'+3y=0,y(0)=7,y^'(0)=11 ?

The solution for y^{''}-4y^'+3y=0,y(0)=7,y^'(0)=11 is y=2e^{3t}+5e^t

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y^{''}-4y^'+3y=0,y(0)=7,y^'(0)=11

y^{^{''}} - 4 y^{^{'}} + 3 y = 0, y (0) = 7, y^{^{'}} (0) = 11

y = 2 e^{3 t} + 5 e^{t}

Solution steps

y^{''} (t) - 4 y^{'} (t) + 3 y = 0

Solve linear ODE:

y = 2 e^{3 t} + 5 e^{t}

y = 2 e^{3 t} + 5 e^{t}

16 y^{^{''''}} + 48 y^{^{''}} + 36 y = 0

y^{^{''}} + 4 y^{^{'}} + 4 y = 0, y (0) = 11

\frac{d ^{2} y}{d x ^{2}} + 2 y = 0

x^{^{''}} + 6 x = 0

y^{^{''}} + y = 0, y (\frac{π}{3}) = 10, y^{^{'}} (\frac{π}{3}) = - 20

What is the solution for y^{''}-4y^'+3y=0,y(0)=7,y^'(0)=11 ?
The solution for y^{''}-4y^'+3y=0,y(0)=7,y^'(0)=11 is y=2e^{3t}+5e^t